Your needs at your budget are a pretty tough row to hoe.
http
/pcpartpicker.com/p/XFXgNG
I came up with this on PCPartpicker.
If you need to buy a copy of windows with it you can shave some cost by going to the non-K version of the processor and using a cheaper motherboard like the Gigabyte PRO4.
Eitherway you will have to build it yourself if you want decent gaming and an i7 processor. You will never get there buying prebuilt at your price point.